A variable is a symbol that appears in algorithms, formulas, and mathematical functions and can receive different values. They are classified according to their particular characteristics in different ways. Discrete variable in research

The variables can be random, continuous, dependent, independent, quantitative, qualitative, among others. This time we are going to know the **discrete variables** .

## Definition of discrete variable

A discrete variable is known as one that **presents the conditions to accept values** from a certain numerical set, that is, it cannot adopt any value, it only acquires the values of a set.

Noting that between the observable values in this discrete variable there is an unlikely distance to be completed with intermediate values, then there can be at least one unobservable value between two values.

In other words, discrete variables are numerical variables with a recordable number of values between any two values. For example, the number of user complaints, the number of registered failures. Discrete variable in research

## Examples of discrete variables

Discrete variables are always quantitative or numerical, for example:

- The number of women in a family.
- The number of fingers we have.
- The number of fouls that occurred during a soccer game.
- The number of people who attend an emergency at a clinic.
- Number of trees in a park.
- Number of television channels that you can watch at home.
- Number of employees of a company.
- Number of books sold monthly on Amazon.
- Number of people who visit a supermarket per day.

## Difference between continuous variable and discrete variable

The quantity of a dimension is determined by comparing it with another quantity (unit) of the same dimension. Discrete variable in research

A variable is continuous if it reaches infinite values between any finite interval. On the contrary, a variable is discrete if within any finite interval it only achieves finite values.

A continuous quantity is determined by the measurement method. The continuous measurement method consists of counting the times that a quantity is greater or less than a unit quantity. Example: The temperature of a patient is measured with the thermometer and can be higher or lower at certain times. It can vary from 37 to 39.5.

A discrete quantity is determined by enumeration. This method of enumeration consists of counting the unit quantities contained. Example: The discrete magnitude of a soccer team is determined by counting the player units that it has, which are 11 players.

An essential characteristic that differentiates a discrete variable from a continuous variable is that the continuous variable is never measured with the same accuracy of a discrete variable, the observed value will depend on the precision of the measuring instrument used. So when measuring a continuous variable, a measurement error can inevitably occur, for example: a person’s temperature can be 37.6, 37.8, 38. Discrete variable in research

It is worth noting that these two are part of a group of variables known as quantitative variables.

## Discrete probability distribution

A probability distribution for a discrete variable is an exclusive list of possible numerical outcomes, such that the specific probability of occurrence is associated with each outcome.

The expected value of the random discrete variable turns out to be a weighted average of the possible outcomes, where each of the weights results from the probabilities associated with each outcome. Discrete variable in research

Where:

**Xi = i – th result of X, the discrete variable of interest.**

**P (Xi) = probability of occurrence of i-th result of X**

The i-th term represents the rule that determines the way in which the terms of the same are calculated. The n-element i-th order statistic is the smallest i-th element. The minimum or first order.

The variance of a random discrete variable (s 2) is specified as the weighted average of the differences between the possible outcomes and their mean.

A random variable X is a function that associates a real number to the different points of the sample space. Discrete variable in research

The discrete variable is also known as a discontinuous variable, it produces a result of finite quantities of predetermined values, which makes its path finite.

Finally, it is said that a discrete variable X has a set of defined possible values x1, x2, x3, xn with probabilities p1, p2, p3, pn., That is, it is only allowed to accept certain values within a variation field determined.

In general, a discrete variable represents the results of a sample in such a way that by P (X = x) we understand the probability of X of reaching the value of x. Then by considering the values of this variable it is possible to develop a mathematical equation that assigns a probability to the different realizations of x of the random X.

In statistical sciences a variable is a measure that has the facility to fluctuate susceptibly to adopt various values that can be observed, it is important to keep in mind that these variables acquire a value when related to other variables, forming part of some hypothesis or theory.